Systems and methods for modeling changes in patient-specific blood vessel geometry and boundary conditions

ABSTRACT

Systems and methods are disclosed for modeling changes in patient-specific blood vessel geometry and boundary conditions resulting from changes in blood flow or pressure. One method includes determining, using a processor, a first anatomic model of one or more blood vessels of a patient; determining a biomechanical model of the one or more blood vessels based on at least the first anatomic model; determining one or more parameters associated with a physiological state of the patient; and creating a second anatomic model based on the biomechanical model and the one or more parameters associated with the physiological state.

RELATED APPLICATION(S)

This application claims priority to U.S. Provisional Application No.61/969,573 filed Mar. 24, 2014, the entire disclosure of which is herebyincorporated herein by reference in its entirety.

FIELD OF THE INVENTION

Various embodiments of the present disclosure relate generally tomedical modeling and related methods. More specifically, particularembodiments of the present disclosure relate to systems and methods formodeling changes in patient-specific blood vessel geometry and boundaryconditions resulting from changes in blood flow or pressure.

BACKGROUND

Coronary artery disease may cause the blood vessels providing blood tothe heart to develop lesions, such as a stenosis (abnormal narrowing ofa blood vessel). As a result, blood flow to the heart may be restricted.A patient suffering from coronary artery disease may experience chestpain, referred to as chronic stable angina during physical exertion orunstable angina when the patient is at rest. A more severe manifestationof disease may lead to myocardial infarction, or heart attack.

A need exists to provide more accurate data relating to coronarylesions, e.g., size, shape, location, functional significance (e.g.,whether the lesion impacts blood flow), etc. Patients suffering fromchest pain and/or exhibiting symptoms of coronary artery disease may besubjected to one or more tests that may provide some indirect evidencerelating to coronary lesions. For example, noninvasive tests may includeelectrocardiograms, biomarker evaluation from blood tests, treadmilltests, echocardiography, single positron emission computed tomography(SPECT), and positron emission tomography (PET). These noninvasivetests, however, typically do not provide a direct assessment of coronarylesions or assess blood flow rates. The noninvasive tests may provideindirect evidence of coronary lesions by looking for changes inelectrical activity of the heart (e.g., using electrocardiography(ECG)), motion of the myocardium (e.g., using stress echocardiography),perfusion of the myocardium (e.g., using PET or SPECT), or metabolicchanges (e.g., using biomarkers).

For example, anatomic data may be obtained noninvasively using coronarycomputed tomographic angiography (CCTA). CCTA may be used for imaging ofpatients with chest pain and involves using computed tomography (CT)technology to image the heart and the coronary arteries following anintravenous infusion of a contrast agent. However, obtaining anatomicdata using CCTA often means that models based on the anatomic datareflect a patient's state as he/she is undergoing imaging (e.g., CCTAimaging). Therefore, anatomic models for assessing blood flow rates arebased on patient conditions during an imaging procedure. For example,patient-specific anatomic models for simulating arterial blood flow areoften obtained while a patient is in a baseline condition during imagingand prior to treatment. However, various forms of treatment may affectanatomy and consequently, blood flow.

In other words, a patent's state may change due to any array of medicalprocedures and/or health conditions. Meanwhile, models for assessingblood flow may fail to reflect the change in state. As a result, thereis a need for methods and systems accounting for changes in a patient'sphysiological state in indirect assessments of blood flow rates. Inparticular, there is a need for methods and systems for creating ananatomical model based on a patient's change in state in order toimprove the accuracy of a simulation performed using the model. Morespecifically, creating an anatomical model may entail modeling changesin patient-specific blood vessel geometry and boundary conditions.

The foregoing general description and the following detailed descriptionare exemplary and explanatory only and are not restrictive of thedisclosure.

SUMMARY

According to certain aspects of the present disclosure, systems andmethods are disclosed for anatomical modeling. One method includes:determining, using a processor, a first anatomic model of one or moreblood vessels of a patient; determining a biomechanical model of the oneor more blood vessels based on at least the first anatomic model;determining one or more parameters associated with a physiological stateof the patient; and creating a second anatomic model based on thebiomechanical model and the one or more parameters associated with thephysiological state.

In accordance with another embodiment, a system for anatomical modelingcomprises: a data storage device storing instructions for anatomicalmodeling; and a processor configured for: determining, using aprocessor, a first anatomic model of one or more blood vessels of apatient; determining a biomechanical model of the one or more bloodvessels based on at least the first anatomic model; determining one ormore parameters associated with a physiological state of the patient;and creating a second anatomic model based on the biomechanical modeland the one or more parameters associated with the physiological state.

In accordance with yet another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for anatomical modeling isprovided. The method includes: determining, using a processor, a firstanatomic model of one or more blood vessels of a patient; determining abiomechanical model of the one or more blood vessels based on at leastthe first anatomic model; determining one or more parameters associatedwith a physiological state of the patient; and creating a secondanatomic model based on the biomechanical model and the one or moreparameters associated with the physiological state.

Additional objects and advantages of the disclosed embodiments will beset forth in part in the description that follows, and in part will beapparent from the description, or may be learned by practice of thedisclosed embodiments. The objects and advantages of the disclosedembodiments will be realized and attained by means of the elements andcombinations particularly pointed out in the appended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the disclosed embodiments, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate various exemplary embodiments andtogether with the description, serve to explain the principles of thedisclosed embodiments.

FIG. 1 is a block diagram of an exemplary system and network formodeling changes in patient-specific blood vessel geometry and boundaryconditions, according to an exemplary embodiment of the presentdisclosure.

FIG. 2 is a block diagram of an exemplary method of changing geometryand boundary conditions in a blood flow simulation arising fromdifferent states of a patient, according to an exemplary embodiment ofthe present disclosure.

FIG. 3 is a block diagram of an exemplary method of determining a secondstate model of conditions, according to an exemplary embodiment of thepresent disclosure.

FIG. 4 is a block diagram of an exemplary method of determining anupdated geometric model based on the second state conditions, accordingto an exemplary embodiment of the present disclosure.

FIG. 5 is a block diagram of an exemplary method of determining geometryresponses to different physiologic conditions, according to an exemplaryembodiment of the present disclosure.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the exemplary embodiments of theinvention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

Often, patient-specific anatomic models for simulating arterial bloodflow are based on image data associated with one state. In one example,coronary artery anatomic data may be obtained under baseline or restingconditions. In another example, coronary artery anatomic data may beobtained based on an anatomic state achieved during imaging, includingstates that increase blood vessel size and blood flow to improve imagequality. Geometric models may be created and boundary conditionsassigned based on the image data from a baseline condition or imagingconditions. Simulations modeling reversible, physiological states (e.g.,blood flow simulations associated with drugs, exercise, and/ortreatment) are often performed based on the anatomic and geometric modelassociated with the first state. However, drugs, exercise, and/ortreatment may all cause changes in blood vessel geometry and boundaryconditions from the first state. For example, a geometry of a patient'sanatomy may change due to various conditions or treatments, includingadministration of drugs (e.g., adenosine or other drugs to increaseblood flow), simulations of medical conditions (e.g., simulatedhyperemia), simulations of physical activities or conditions (e.g.,exercise), angioplasty, surgery (e.g., stenting or bypass grafting),etc. Therefore, a desire exists for patient-specific models forsimulating arterial blood flow that may account for a representation ofa patient's state, where the patient's state may differ from a statefrom which the anatomic model was built. Simulating arterial blood flowusing a patient-specific model reflecting a second state may improveaccuracy of simulation results. Particularly, the present disclosure isdirected to second state(s) that may include reversible, physiologicalstates. Furthermore, simulations and models based on the second statemay further be applied to model possible treatments that may affectgeometry (e.g., angioplasty, stenting, and/or bypass surgery). Forexample, a geometric change to a model may be made (e.g., to modelstenting), based on patient-specific models that reflect a second state.The following discussion outlines various scenarios where an anatomicand biomechanical model under which simulations are performed, may notaccurately represent a patient's state.

In one embodiment, simulations may be performed using patient-specificanatomic models based on image data obtained under resting conditions.Geometric models and boundary condition models based on these baselineconditions may then be used as input to computer models in order topredict flow and pressure under a physiologic state, including duringthe administration of adenosine or other drugs to increase blood flowand simulate exercise, or after angioplasty and stenting or bypassgrafting. The patient's anatomy may be at a state distinct from thefirst, resting state, in light of one or more treatments or conditions.Therefore, a desire exists for patient-specific models for simulatingarterial blood flow to take into account a second state reflectingpatient anatomy at a non-resting state.

In another embodiment, a patient-specific model extracted from imagedata may be based on a state distinct from a baseline state. Forinstance, in the case of coronary artery anatomic data, beta blockersmay be used to reduce heart rate, while nitrates may be administered todilate large coronary arteries. Both drugs may be administered toimprove image quality. For example, beta blockers used to slow the heartmay affect blood pressure and hence, the size of a vessel; and nitratesused during coronary computed tomography (CT) angiography may increaseflow by relaxing smooth muscle cells in blood vessels, decreasing theirtension (or tone), and increasing the size of the blood vessels. Theincreased size and flow through the vessels improves image quality. Theadministration of beta blockers and/or nitrates may cause geometry andphysiologic conditions to change to a state that may be different from abaseline state. However, the new state of the arteries from theadministration of beta blockers and/or nitrates changes geometry andphysiologic conditions to a state that may be different from a baseline.In other words, modeled changes in blood flow and pressure may causechanges in patient-specific geometric models and boundary conditions,since local vessel size may be affected by local pressure and smoothmuscle tone of the vessels (which can be affected by administration ofnitrates, adenosine, papaverine, adenosine triphosphate (ATP), etc.).However, an image created from baseline conditions may not account forthe affect that drugs may have on anatomy geometry and boundaryconditions. A blood flow simulation performed under the state may beexpected to yield diagnostic data different from that attained prior tothe administration of the drugs. Thus, the present disclosure isdirected to a new approach including changing geometry and boundaryconditions in a blood flow simulation to model an original baseline orresting state of arteries prior to administration of drugs.

A specific example of the above embodiment may include modeling ofincreased flow as occurs during simulated hyperemia. Such modeling maybe performed to calculated fractional flow reserve or coronary flowreserve. The simulations of increased flow may be typically performedbased on coronary anatomic data obtained under baseline or restingconditions. In reality, the data is often obtained subsequent toadministration of beta blockers and/or nitrates. More specifically,simulation of increased blood flow through coronary arteries may resultin pressure changes along the coronary arteries, especially downstreamof a coronary artery stenosis. The metric of FFR may be calculated fromthe ratio of downstream pressure to aortic pressure. As a result duringthe simulation of hyperemia (performed using anatomic data obtained atbaseline), blood pressure may be significantly lower at pointsdownstream of the vessel rather than at points upstream of the vessel.Also, blood pressure may be significantly lower during the hyperemicstate than during the resting state. The blood vessels may diminish insize (i.e., “deflate”) due to the reduced pressure. Such changes invessel size may affect tightness of a coronary artery stenosis or thecaliber of vessels downstream from the stenosis. This in turn may affectthe accuracy of the hyperemic simulation and accuracy of the predictedFFR, as compared to measured data (obtained during actual administrationof vasodilators causing increased flow and pressure reduction along thelength of the vessel). Thus, the present disclosure is directed to a newapproach for changing geometry and boundary conditions in a blood flowsimulation model of the hyperemic state of arteries using image dataobtained without administration of drugs to increase blood flow.

Furthermore, treatment recommendations may be improved with modelingtaking into account changes in patient-specific blood vessel geometryand boundary conditions. For example, percutaneous coronary intervention(PCI) or coronary artery bypass grafting (CABG) is often used to treatpatients with coronary artery disease. Computer models are often used topredict changes in blood flow or pressure resulting from the treatmentsto aid the physician in deciding how best to treat a given patient.Patient-specific models for simulating PCI or CABG may be created frompre-treatment image data, then modified to incorporate a treatment plan.The modifications are generally restricted to geometric changes indiseased segments to account for dilation of stenosis with PCI orcreation of an alternate conduit for blood flow with CABG. However,treatments may affect more than simply diseased segments. Treatmentspotentially change blood flow and pressure in an entire coronary arterytree. Therefore, the present disclosure is further directed to a newapproach for modeling geometric changes and boundary condition changessecondary to changes in blood flow or pressure resulting from treatmentsfor arterial disease. For example, the present disclosure may includeupdating geometric model and boundary conditions (created frompre-treatment data) to account for new post-treatment flow and pressure.In other words, the present disclosure may include changing geometry andboundary conditions in a blood flow simulation to model post-treatmentstate of arteries due to predicted changes in blood flow and pressurefrom models originally created using image data obtained prior totreatment.

In a broader sense, the present disclosure is directed to a new approachfor systems and methods for modeling changes in patient-specific bloodvessel geometry and boundary conditions based on changes in blood flowor pressure.

Referring now to the figures, FIG. 1 depicts a block diagram of anexemplary system and network for modeling changes in patient-specificblood vessel geometry and boundary conditions. Specifically, FIG. 1depicts a plurality of physicians 102 and third party providers 104, anyof whom may be connected to an electronic network 100, such as theInternet, through one or more computers, servers, and/or handheld mobiledevices. Physicians 102 and/or third party providers 104 may create orotherwise obtain images of one or more patients' cardiac and/or vascularsystems. The physicians 102 and/or third party providers 104 may alsoobtain any combination of patient-specific information, such as age,medical history, blood pressure, blood viscosity, etc. Physicians 102and/or third party providers 104 may transmit the cardiac/vascularimages and/or patient-specific information to server systems 106 overthe electronic network 100. Server systems 106 may include storagedevices for storing images and data received from physicians 102 and/orthird party providers 104. Server systems 106 may also includeprocessing devices for processing images and data stored in the storagedevices.

FIG. 2 is a block diagram of an exemplary method 200 of changinggeometry and boundary conditions in a blood flow simulation to model asecond state of a patient different from a first state of the patient(e.g., from the state in which the patient was imaged), according to anexemplary embodiment. The second state, for example, may be (1) aresting state, free of the administration of drugs used during imaging,(2) a hyperemic state of arteries, free of drugs used to increase bloodflow, (3) a post-treatment state, or (4) any other desired state.

In one embodiment, step 201 may include constructing a patient-specificanatomic model. In one embodiment, the model may be from two-dimensionalimaging modalities (e.g., coronary angiography, biplane angiography,etc.) or three-dimensional imaging modalities (e.g., 3-D rotationalangiography, coronary computed tomographic angiograph (cCTA), magneticresonance angiography (MRA)). Step 201 may further include directlysegmenting image data and creating a patient-specific three-dimensionalanatomic model of the patient's arteries. Alternately or in addition,step 201 may involve modifying a previously-constructed “generic” model,customizing the model for a particular patient, and creating apatient-specific model. In yet another embodiment, step 201 may includeproviding, receiving, and/or loading a patient-specific anatomic modelof a patient into a computer. For example, the model may be from anelectronic storage device (e.g., a hard drive, network drive, etc.). Inone embodiment, the model may represent a first, baseline state of apatient.

In any or all of the embodiments of step 201, the patient-specificanatomic model may include information related to arteries of interest,including the length of each segment, diameter along the length of asegment (or any other geometric description of the segment), branchingpatterns, presence of disease, characteristics of disease (includingcomposition of atherosclerotic plaques), etc. A representation of thepatient-specific model may be defined by a surface enclosing athree-dimensional volume, a one-dimensional model where the centerlineof the vessels is defined together with cross-sectional area informationalong the length, and/or an implicit representation of a vessel surface.

In one embodiment, step 203 may include defining physiologic conditionsassociated with blood flow and pressure that reflect a patient'scondition at the time that imaging was taken. Conditions at the time ofimaging may make up a “first (physiological) state” for a patient. Forexample, a patient may be administered beta blockers to lower his heartrate and/or sublingual nitrates to dilate his coronary arteries in orderto improve image quality. Step 203 of determining physiologic conditionsmay include determining and/or assigning aortic pressure conditions andresistance of coronary artery microcirculation based on a patient'sintake of beta blockers and/or nitrates.

In one embodiment, step 205 may include creating a biomechanical modelof a vessel wall, for example, generating a biomechanical model for eachsegment of artery extracted in the patient-specific anatomic model ofstep 201. In one embodiment, the vessel wall model may be based onone-dimensional elastic or viscoelastic models of blood vessels. Suchmodels may include models that typically relate pressure to vesselcross-sectional area along the length of a vessel. Exemplary models aredescribed in Olufsen et al. (Olufsen M S. “Structured tree outflowcondition for blood flow in larger systemic arteries.” Am J PhysiolHeart Circ Physiol 276:H257-H268, 1999.), Wan et al. (J. Wan, B. N.Steele, S. A. Spicer, S. Strohband, G. R. Feijoo, T. J. R. Hughes, C. A.Taylor (2002) “A One-dimensional Finite Element Method forSimulation-Based Medical Planning for Cardiovascular Disease.” ComputerMethods in Biomechanics and Biomedical Engineering. Vol. 5, No. 3, pp.195-206), and Raghu et al. (R. Raghu, I. E. Vignon-Clementel, C. A.Figueroa, C. A. Taylor (2011) “Comparative Study of ViscoelasticArterial Wall Models in Nonlinear One-dimensional Finite ElementSimulations of Blood Flow.” Journal of Biomechanical Engineering, Vol.133, No. 8, pp 081003). Alternately, biomechanical models of vessel wallmay represent the vessel wall as a surface with spatially-varyingthickness and material properties, for example, as described in Figueroaet al. (C. A. Figueroa, I. E. Vignon-Clementel, K. C. Jansen, T. J. R.Hughes, C. A. Taylor (2006) “A Coupled Momentum Method For ModelingBlood Flow In Three-Dimensional Deformable Arteries.” Computer Methodsin Applied Mechanics and Engineering, Vol. 195, Issues 41-43, pp.5685-5706.) or in Figueroa et al. (C. A. Figueroa, S. Baek, C. A.Taylor, J. D. Humphrey (2009) “A Computational Framework for CoupledFluid-Solid Growth Modeling in Cardiovascular Simulations.” ComputerMethods in Applied Mechanics and Engineering, Vol. 198, No. 45-46, pp.3583-3602). Another example of a biomechanical model may include a bloodvessel as a three-dimensional continuum model, as in Gee et al. (Gee MW, Förster C, Wall W A (2010) “A computational strategy for prestressingpatient-specific biomechanical problems under finite deformation.” Int JNumer Methods Biomed Eng 26 (1):52-72), Gerbeau et al. (Gerbeau J-F,Vidrascu M, Frey P (2005) “Fluid-structure interaction in blood flows ongeometries based on medical imaging.” Comput Struct 83 (2-3):155-165),or as in Kioussis et al. (Kiousis D E, Gasser T C, Holzapfel G A. 2007.“A numerical model to study the interaction of vascular stents withhuman atherosclerotic lesions.” Ann. Biomed. Eng. 35:1857-69). Materialproperties of vessel walls may be defined based on population averagedmaterial properties, imaging data, and/or data inferred by experimentalmeasurement of deformation of coronary arteries during a cardiac cycleand solving an inverse optimization problem to estimate the bestconstitutive fit consistent with data. Examples of constitutive modelsinclude linear elastic, hyperelastic, linear and nonlinear viscoelasticmodels including those discussed in Wan et al. (J. Wan, B. N. Steele, S.A. Spicer, S. Strohband, G. R. Feijoo, T. J. R. Hughes, C. A. Taylor(2002) A One-dimensional Finite Element Method for Simulation-BasedMedical Planning for Cardiovascular Disease. Computer Methods inBiomechanics and Biomedical Engineering. Vol. 5, No. 3, pp. 195-206),Raghu et al. ([R. Raghu, I. E. Vignon-Clementel, C. A. Figueroa, C. A.Taylor (2011) Comparative Study of Viscoelastic Arterial Wall Models inNonlinear One-dimensional Finite Element Simulations of Blood Flow.Journal of Biomechanical Engineering, Vol. 133, No. 8, pp 081003.) andTaylor et al. (C. A. Taylor, J. D. Humphrey (2009) Open Problems inComputational Vascular Biomechanics: Hemodynamics and Arterial WallMechanics. Computer Methods in Applied Mechanics and Engineering, 198,No. 45-46, pp. 3514-3523). These material models may be purelyphenomenological stress-strain relations or phenomenological models thatare based on the microstructure of blood vessels, e.g. including data oncollagen and elastin fiber orientation derived from experimental data,see for example Humphrey et al. (J. D. Humphrey, Cardiovascular SolidMechanics: Cells, Tissues, and Organs, Springer, New York, 2002.) andHolzapfel et al. (G. A. Holzapfel, T. C. Gasser, R. W. Ogden, A newconstitutive framework for arterial wall mechanics and a comparativestudy of material models, J. Elasticity (2000) 1-48).

In one embodiment, an elastic modulus of a vessel wall may be roughlyestimated from a Hounsfield unit (HU) of tissue surrounding a lumenboundary. Thickness of a vessel wall may be estimated from image dataand/or approximated by a theoretical relationship between vessel radiusand wall thickness, e.g., assuming the thickness is ⅕^(th) or 1/10^(th)of the radius. Vessel wall models may represent material behaviorpassively or may include active behavior to model tension due to smoothmuscle tone in the vessel wall. The material properties may be affectedby pressure, flow, wall shear stress, wall tensile stress, and/orvasoactive drugs that may alter tension in the vessel wall (e.g., byinducing smooth muscle cell contraction or relaxation).

In one embodiment, steps 201-205 of determining a patient-specificgeometrical model, a physiologic model, and a biomechanical model mayall pertain to a “first state.” In some embodiments, such a first-statemodel may represent the patient's conditions when imaging was performed.

In one embodiment, step 207 may include defining physiologic conditions,boundary conditions, and/or material properties of a patient in a secondstate, other than the first state. For example, physiologic conditionsand boundary conditions of a patient under hyperemic conditions may bedefined using a method described in U.S. Pat. No. 8,315,812 issued Nov.20, 2012, the entire disclosure of which is hereby incorporated byreference in its entirety. The physiologic conditions and boundaryconditions of a patient after treatment may be defined using the methoddescribed in U.S. Pat. No. 8,249,815 issued Aug. 21, 2012, the entiredisclosure of which is hereby incorporated in reference in its entirety.In one embodiment, changes in elastic properties of a blood vessel maybe modified for a second state based on an expected response tomedications (e.g., nitrates). For example, if nitrates were used duringimaging of a patient, a second state may include determining vasoactiveresponse of arteries in response to a “removal” of nitrates. The secondstate may thus include vasoconstriction of arteries relative to thefirst state, which may closer model a patient's anatomy and/orphysiology under resting conditions. In some embodiments, step 207 mayinclude determining changes in properties based on data in literature.For example, an expected response of nitrates known in literature, is anincrease in diameters of 0% to 30%, depending on the size of a vesseland whether it is healthy or diseased. In another embodiment, if imagedata is available for a population of patients with and withoutnitrates, changes in vessel size due to administration of nitrates maybe determined using machine learning methods. The data may then be usedto update vessel properties for the second state of the patient. FIG. 5,described further herein, provides further detail on machine learningmethods for determining changes in geometry with respect to variousstates.

In one embodiment, step 209 may include generating an anatomic model ofthe second state, based on flow and pressure conditions of the patientin a second state. In one embodiment, step 209 may include updatingand/or revising a patient-specific first-state model (e.g., thepatient-specific anatomic model from step 201). For example, step 209may include simulating blood flow and pressure of the patient in thesecond state, using the patient-specific anatomic model andbiomechanical model of the patient in the first state. In other words,step 209 may include simulating blood flow and pressure in thefirst-state model, along with boundary conditions and/or materialproperties associated with the second-state model. Further detailregarding step 209 is provided in FIGS. 3 and 4.

In one embodiment, step 211 may include performing simulations using amodel reflecting a patient's second state. For example, step 211 mayinclude performing a simulation of blood flow and pressure using thesecond-state model. Furthermore, step 213 may include providing and/oroutputting results of the simulation in the form of a report via acomputer output device.

FIG. 3 is a block diagram of an exemplary method 300 of determining asecond-state model of conditions, according to an exemplary embodiment.In one embodiment, step 301 may include determining various availablemodels and/or patient conditions. For example, a second-state model mayinclude (i) an original baseline or resting state of blood vessels(e.g., arteries) prior to administration of drugs (e.g., to improveimage data), (ii) a hyperemic state subsequent to administration of adrug to increase blood flow (e.g., adenosine, papaverine, ATP,Regadenoson, etc.), (iii) a simulated exercise state, (iv) apost-treatment state, etc. In one embodiment, step 303 may includedetermining which of the available models is of interest. For example,step 303 may include selecting one or more of the available models as asecond-state model based on user selection, inferences from inputassociated with the first-state model, patient information, etc.

In one embodiment, step 305 may include determining conditionsassociated with the selected model. For example, in response to ahyperemic state, physiologic condition changes may include: aorticpressure decreases, heart rate increases, vascular microcirculatoryresistance decreases, healthy arteries dilating in response to flow,stenosis or segments of arteries downstream of disease reducing in sizein response to pressure changes, etc. In another example, a response toa simulated exercise state may include the following physiologiccondition changes: cardiac output increases, aortic pressure increases,heart rate increases, vascular microcirculatory resistance decreases,healthy arteries' dilation in response to flow, stenosis or segments ofarteries downstream of disease reducing in size in response to pressurechanges, etc. For a post-treatment state, for example subsequent totreatment including angioplasty and stenting or bypass surgery, localblood pressure and flow along an arterial tree may be altered forresting conditions and high flow conditions (e.g., hyperemia, exercise,etc.).

In one embodiment, step 307 may include computing forces on blood vesselwalls for the second state. For example, step 307 may include simulatingblood flow and pressure in the first-state model and using results ofthe simulation to modify physiologic boundary conditions to representthose of the second state. In one embodiment, step 307 may be performedusing, for example, (i) a reduced order model (e.g., a lumped-parameteror one-dimensional wave propagation model), (ii) a three-dimensionalfinite element, finite volume, lattice Boltzman, level set, immersedboundary, or particle-based method to solve 3-D equations of blood flowand pressure, or (iii) a fluid-structure interaction method to solve forblood flow, pressure, and vessel wall motion.

FIG. 4 is a block diagram of an exemplary method 400 of determining anupdated geometric model based on the second-state conditions, accordingto an exemplary embodiment. In other words, method 400 may be directedat determining a geometric model based on a biomechanical model of apatient's arteries (e.g., a model from method 300). In one embodiment,step 401 may include determining a relationship between geometry andbiomechanical properties. For example, step 401 may include determiningone or more one-dimensional elastic and/or viscoelastic models of bloodvessels relating pressure to vessel cross-sectional area along thelength of a vessel. In such a case, a representative pressure diametercurve may be calibrated to match pre-treatment pressure-diameter valuesat different centerline points. Then, a new lumen diameter may beestimated by probing the diameter of the calibrated curve at the newpressure. Alternatively, step 401 may include solving stress-equilibriumequations for a computational model of the vessel wall, with thepressure difference between the first state and the second state actingin the inner wall and a zero traction boundary condition acting on theouter surface of the vessel.

In one embodiment, step 403 may include solving the models and/orequations from step 401 to determine geometry based on the biomechanicaldata. For example, step 403 may include solving for geometry correctioniteratively along with computational fluid dynamics (CFD) (e.g., usingpredictor-corrector methods). Such a method of determining the geometrymay be possible because changes in geometry affect flow rate and bloodpressure. Alternatively, geometry may be solved for in a coupled mannerusing an arbitrary Lagrangian-Eulerian framework. In another example, ifexperimental data relating changes in geometry to different physiologicconditions is available, machine learning methods may be used to modelhow cross-sectional area of vessels change locally, given a change inpressure and surrounding geometry. In some cases, training data fromother patients may be used to inform the model to predict area changesfrom pressures computed in method 300.

In one embodiment, step 405 may include determining a deformation thatmay be computed to update the geometrical model. For example, step 405may include determining a minimal deformation that creates asegmentation with desired cross-sectional area at each location, thatmay then be computed to update a geometry. For example, the flow domainand vessel walls may be represented by an explicit mesh. This explicitmesh may be modified by a variety of elastic deformation techniques.Alternatively, a flow domain may have an implicit representationdeformed by a speed function using a level set method. A level setmethod may permit tracking shapes by building a surface fromtwo-dimensional boundaries of shapes, where the shapes may include level“slices” of the surface. For example, a speed function may be used tochange a representation for a level set method defined by computeddesired cross sectional areas along the centerline. The speed functionfor a level set method may include terms to control the curvature of theimplicit surface as it is modified from the first state to the secondstate. Step 407 may include producing a patient-specific anatomic modelto represent a patient in second state conditions. Producing thesecond-state model may include updating a first-state geometric model.For example, step 407 may include deforming an implicit representation.Step 407 may further include determining whether to mesh the implicitrepresentation with other representations or use the implicitrepresentation directly. Step 409 may include using either a mesh ofmultiple implicit representations or a single implicit representation ofmodified boundary conditions for display, calculations of CFD equations,or a combination thereof. For example, step 409 may include performing asimulation of blood flow and pressure using the second-statepatient-specific anatomic model and/or biomechanical model. In a furtherexample, step 409 may include providing information based on thesimulation to a user, for instance, through a report or display via acomputer output device.

In one embodiment, method 400 may include further modeling geometricchanges based on post-treatment states (e.g., angioplasty, stenting, orbypass surgery). For example, deforming the mesh for an anatomic modelin step 407 may include accounting for a geometry of a stent or ageometry post-angioplasty. Then, a simulation of step 409 may includesimulating blood flow and pressure through the anatomic models builtfrom physiologic state boundary conditions and geometry, as well astreatment-related geometry. As a further step, results from thesimulations may be output or displayed. For example, such output mayinclude a treatment recommendation, where several simulations may be runto simulate various treatment options.

FIG. 5 is a block diagram of an exemplary method 500, such as machinelearning methods, of determining geometry responses to differentphysiologic conditions, according to an exemplary embodiment. In oneembodiment, step 501 may include determining information of a populationof patients (e.g., patient age, gender, physical conditions, height,weight, diet, family medical history, etc.). Step 503 may includedetermining image and/or experimental data associated with thepopulation of patients. For example, the image and/or experimental datamay characterize the population of patients as a group. Alternately,image and/or experimental data may include data respective to eachpatient in the population of patients.

In one embodiment, step 505 may include determining or calculating avalue of interest associated with the image and/or experimental data.For example, a value of interest may be a measurement (e.g., materialproperties of a vessel wall) and/or a change in a measurement (e.g.,changes in vessel size due to administration of a nitrate). In any case,step 505 may include computing, for each patient in a population ofpatients, the value of interest. Step 505 may further include averagingthe values for an entire population of patients. Step 507 may theninclude predicting a change in geometry based on the values given by thepopulation of patients. For example, step 507 may include using thevalues from step 505 to model how cross-sectional area of a vesselchanges locally, given change in pressure and surrounding geometry. Step507 may then help predict area changes from pressures computed bybiomechanical modeling based on physiologic conditions.

Various embodiments of the present disclosure relate to medical modelingand related methods, specifically, modeling changes in patient-specificanatomic models. For example, the present disclosure includescalculating blood flow and pressure in patient-specific arterial modelsupdated to reflect geometric and boundary condition changes. In someembodiments, the changes arise from a state change subsequent a state ofa patient in which imaging was performed. Some instances of applicationsfor such modeling include (i) resting, exercise, or hyperemic conditionsusing image data obtained subsequent administration of nitrates and/orbeta blockers and/or (ii) post-treatment conditions using image dataobtained prior to treatment. The present disclosure describes thesystems and methods directed to coronary arteries, but the disclosuremay also apply to simulations of blood flow and pressure in any arterialtree including but not limited to the carotid, cerebral, renal, andlower extremity arteries.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

What is claimed is:
 1. A computer-implemented method of anatomicalmodeling, the method comprising: receiving image data of one or moreblood vessels of a patient, the image data being obtained while thepatient's body is at a first physiological state; determining, using aprocessor, a patient-specific anatomic model of the one or more bloodvessels from the image data obtained while the patient's body is at thefirst physiological state; determining a patient-specific biomechanicalmodel of the one or more blood vessels from the image data obtainedwhile the patient's body is at the first physiological state;determining a second physiological state of the patient's body differentfrom the first physiological state, wherein the second physiologicalstate includes a hyperemic state, an exercise state, or a medicatedstate; determining one or more parameters associated with the secondphysiological state of the patient's body; and updating the anatomicmodel by incorporating one or more geometric changes associated with theone or more parameters of the second physiological state of thepatient's body and the biomechanical model.
 2. The method of claim 1,further comprising: determining one or more blood flow characteristicsdefining the flow of blood through the updated anatomic model.
 3. Themethod of claim 1, wherein the one or more parameters are associatedwith physiologic conditions, boundary conditions, or a combinationthereof.
 4. The method of claim 1, further comprising: performing asimulation using the biomechanical model, wherein the one or moreparameters associated with the second physiological state of the patientare determined using the simulation.
 5. The method of claim 4, whereinthe simulation includes a simulation of blood flow and pressure.
 6. Themethod of claim 1, further comprising: selecting one or more portions ofthe anatomic model of one or more blood vessels of the image dataobtained while the patient's body is at the first physiological state,wherein the biomechanical model includes a model of one of the one ormore portions of the anatomic model.
 7. The method of claim 1, whereinthe biomechanical model includes at least one of measurements orproperties of a wall of the one or more blood vessels.
 8. The method ofclaim 1, further comprising: performing a simulation using the updatedanatomic model; and outputting results of the simulation.
 9. The methodof claim 1, wherein updating the anatomic model includes determining asecond patient-specific anatomic model.
 10. A system for anatomicalmodeling, the system comprising: a data storage device storinginstructions for anatomical modeling; and a processor configured toexecute the instructions to perform a method including: receiving imagedata of one or more blood vessels of a patient, the image data beingobtained while the patient's body is at a first physiological state;determining, using a processor, a patient-specific anatomic model of theone or more blood vessels from the image data obtained while thepatient's body is at the first physiological state; determining apatient-specific biomechanical model of the one or more blood vessels ofthe image data obtained while the patient's body is at the firstphysiological state; determining a second physiological state of thepatient's body different from the first physiological state, wherein thesecond physiological state includes a hyperemic state, an exercisestate, or a medicated state; determining one or more parametersassociated with the second physiological state of the patient's body;and updating the anatomic model by incorporating one or more geometricchanges associated with the one or more parameters of the secondphysiological state of the patient's body and the biomechanical model.11. The system of claim 10, wherein the system is further configuredfor: determining one or more blood flow characteristics defining theflow of blood through the updated anatomic model.
 12. The system ofclaim 10, wherein the one or more parameters are associated withphysiologic conditions, boundary conditions, or a combination thereof.13. The system of claim 10, wherein the system is further configuredfor: performing a simulation using the biomechanical model, wherein theone or more parameters associated with the second physiological state ofthe patient are determined using the simulation.
 14. The system of claim13, wherein the simulation includes a simulation of blood flow andpressure.
 15. The system of claim 10, wherein the system is furtherconfigured for: selecting one or more portions of the first anatomicmodel of one or more blood vessels of the image data obtained while thepatient's body is at the first physiological state, wherein thebiomechanical model includes a model of one of the one or more portionsof the anatomic model.
 16. The system of claim 10, wherein thebiomechanical model includes at least one of measurements or propertiesof a wall of the one or more blood vessels.
 17. The system of claim 10,wherein the system is further configured for: performing a simulationusing the updated anatomic model; and outputting results of thesimulation.
 18. The system of claim 10, wherein updating the anatomicmodel includes determining a second patient-specific anatomic model. 19.A non-transitory computer readable medium for use on a computer systemcontaining computer-executable programming instructions for performing amethod of anatomical modeling, the method comprising: receiving imagedata of one or more blood vessels of a patient, the image data beingobtained while the patient's body is at a first physiological state;determining, using a processor, a patient-specific anatomic model of theone or more blood vessels from the image data obtained while thepatient's body is at the first physiological state; determining apatient-specific biomechanical model of the one or more blood vessels ofthe image data obtained while the patient's body is at the firstphysiological state; determining a second physiological state of thepatient's body different from the first physiological state, wherein thesecond physiological state includes a hyperemic state, an exercisestate, or a medicated state; determining one or more parametersassociated with the second physiological state of the patient's body;and updating the anatomic model by incorporating one or more geometricchanges associated with the one or more parameters of the secondphysiological state of the patient's body and the biomechanical model.20. The non-transitory computer readable medium of claim 19, the methodfurther comprising: determining one or more blood flow characteristicsdefining the flow of blood through the updated anatomic model.
 21. Thenon-transitory computer readable medium of claim 19, wherein the one ormore parameters are associated with physiologic conditions, boundaryconditions, or a combination thereof.
 22. The non-transitory computerreadable medium of claim 19, the method further comprising: performing asimulation using the biomechanical model, wherein the one or moreparameters associated with the second physiological state of the patientare determined using the simulation.
 23. The non-transitory computerreadable medium of claim 19, wherein updating the anatomic modelincludes determining a second patient-specific anatomic model.
 24. Acomputer-implemented method of anatomical modeling, the methodcomprising: receiving image data of one or more blood vessels of apatient, the image data being obtained while the patient's body is at afirst physiological state; determining, using a processor, apatient-specific anatomic model of the one or more blood vessels of theimage data obtained while the patient's body is at the firstphysiological state, wherein the first physiological state includes ahyperemic state, an exercise state, or a medicated state; determining apatient-specific biomechanical model of the one or more blood vessels ofthe image data obtained while the patient's body is at the firstphysiological state; determining a second physiological state of thepatient different from the first physiological state; determining one ormore parameters associated with the second physiological state of thepatient's body; and updating the anatomic model by incorporating one ormore geometric changes associated with the one or more parameters of thesecond physiological state of the patient's body and the biomechanicalmodel.